Efficient algorithms for the max k-vertex cover problem

  • Authors:

  • Federico Della Croce;Vangelis Th. Paschos

  • Affiliations:

  • D.A.I., Politecnico di Torino, Italy;LAMSADE, CNRS, UMR 7243, PSL Research University, Université Paris-Dauphine, France,Institut Universitaire de France, France

  • Venue:
  • TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
  • Year:
  • 2012

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Abstract

We first devise moderately exponential exact algorithms for maxk-vertex cover, with time-complexity exponential in n but with polynomial space-complexity by developing a branch and reduce method based upon the measure-and-conquer technique. We then prove that, there exists an exact algorithm for maxk-vertex cover with complexity bounded above by the maximum among ck and γτ, for some γτ is the cardinality of a minimum vertex cover of G (note that $\textsc{max $k$-vertex cover}{} \notin \textbf{FPT}$ with respect to parameter k unless $\textbf{FPT} = \textbf{W[1]}$), using polynomial space. We finally study approximation of maxk-vertex cover by moderately exponential algorithms. The general goal of the issue of moderately exponential approximation is to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-case running times importantly smaller than those needed for exact computation, approximation ratios unachievable in polynomial time.